-972-3n+7n^2=0

Solution for -972-3n+7n^2=0 equation:

-972-3n+7n^2=0

a = 7; b = -3; c = -972;
Δ = b2-4ac
Δ = -32-4·7·(-972)
Δ = 27225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27225}=165$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-165}{2*7}=\frac{-162}{14}
=-11+4/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+165}{2*7}=\frac{168}{14}
=12
$